Abstract: In this talk we review theoretical results on the mean-square convergence of numerical methods for stochastic ordinary differential equations, stochastic delay differential equations, neutral stochastic delay differential equations, jump-diffusion differential equations, neutral stochastic delay differential equations with jump-diffusion, stochastic partial differential equations. These results are called fundamental convergence theorems of numerical methods for stochastic differential equations. In this talk we propose a fundamental convergence theorem of semidiscretisation for stochastic Schrödinger equations in temporal direction. And based on Feynman-Kac type formula on backward stochastic differential equations, we present a fundamental convergence theorem of numerical methods for backward stochastic differential equations, and apply it to the mean-square convergence of numerical schemes for backward stochastic differential equations.

 

About the Speaker: Jia-Lin Hong obtained his PhD from Jilin University 1994, he is now a Professor in Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences. His research interests are in the structure‐preserving algorithms, inclusive of deterministic symplectic methods for Hamiltonian systems, deterministic multi‐symplectic methods for Hamiltonian partial differential equations, stochastic symplectic methods for stochastic Hamiltonian systems, stochastic multi-symplectic methods for stochastic Hamiltonian partial differential equations, stochastic conservative methods for stochastic differential equations, etc.

 

Date&Time: December 26, 2014 (Friday), 15:30 - 16:30
Location: 606 Conference Room